(\partial)/(\partial x)((6x-7y)/(6x+7y))

解

\frac{\partial}{\partial x} (\frac{6 x - 7 y}{6 x + 7 y})

\frac{84 y}{( 6 x + 7 y ) ^{2}}

解答ステップ

\frac{\partial}{\partial x} (\frac{6 x - 7 y}{6 x + 7 y})

y

を定数として扱う

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{\partial}{\partial x} ( 6 x - 7 y ) ( 6 x + 7 y ) - \frac{\partial}{\partial x} ( 6 x + 7 y ) ( 6 x - 7 y )}{( 6 x + 7 y ) ^{2}}

\frac{\partial}{\partial x} (6 x - 7 y) = 6

\frac{\partial}{\partial x} (6 x + 7 y) = 6

= \frac{6 ( 6 x + 7 y ) - 6 ( 6 x - 7 y )}{( 6 x + 7 y ) ^{2}}

拡張

6 (6 x + 7 y) - 6 (6 x - 7 y) : 84 y

= \frac{84 y}{( 6 x + 7 y ) ^{2}}